The Drude weight of the spin-1/2 XXZ chain: density matrix renormalization group versus exact diagonalization

Abstract

We revisit the problem of the spin Drude weight D of the integrable spin-1/2 XXZ chain using two complementrary approaches, exact diagonalization (ED) and the time-dependent density-matrix renormalization group (tDMRG). We pursue two main goals. First, we present extensive results for the temperature dependence of D. By exploiting time translation invariance within tDMRG, one can extract D for significantly lower temperatures than in previous tDMRG studies. Second, we discuss the numerical quality of the tDMRG data and elaborate on details of the finite-size scaling of the ED results, comparing calculations carried out in the canonical and grand-canonical ensembles. Furthermore, we analyze the behavior of the Drude weight as the point with SU(2)-symmetric exchange is approached and discuss the relative contribution of the Drude weight to the sum rule as a function of temperature.

Revised version, additional ED and DMRG data for negative Delta, DMRG data for lower temperatures, discussion of Benz et al. 2005 corrected

References in corpus (18)

• The density-matrix renormalization group in the age of matrix product states
• Real time evolution using the density matrix renormalization group
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Spectral functions in one-dimensional quantum systems at T>0
• The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
• A real-time study of diffusive and ballistic transport in spin-1/2 chains using the adaptive time-dependent density matrix renormalization group method
• Spin conductivity in almost integrable spin chains
• Density dynamics in translationally invariant spin-1/2 chains at high temperatures: a current auto-correlation approach to finite time- and length-scales
• Thermal transport of the XXZ chain in a magnetic field
• Negative differential conductivity in far-from-equilibrium quantum spin chains
• Real-time dynamics at finite temperature by DMRG: A path-integral approach
• Drude weight in systems with open boundary conditions
• Finite Drude weight for 1D low temperature conductors
• Spin hydrodynamics in the S = 1/2 anisotropic Heisenberg chain
• Coherent spin-current oscillations in transverse magnetic fields

Cited by in corpus (62)

• Finite-temperature transport in one-dimensional quantum lattice models
• Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
• Quasilocal charges in integrable lattice systems
• Bethe-Boltzmann Hydrodynamics and Spin Transport in the XXZ Chain
• Diffusive and subdiffusive spin transport in the ergodic phase of a many-body localizable system
• Families of quasi-local conservation laws and quantum spin transport
• Super-diffusion in one-dimensional quantum lattice models
• Quantum transport in ultracold atoms
• Non-equilibrium spin transport in integrable spin chains: persistent currents and emergence of magnetic domains
• Real-time and real-space spin- and energy dynamics in one-dimensional spin-1/2 systems induced by local quantum quenches at finite temperatures
• Spin-current autocorrelations from single pure-state propagation
• Universal spin dynamics in infinite-temperature one-dimensional quantum magnets
• Exact Nonequilibrium Steady State of an Open Hubbard Chain
• Exact steady states for quantum quenches in integrable Heisenberg spin chains
• Reducing the numerical effort of finite-temperature density matrix renormalization group transport calculations
• Exactly conserved quasilocal operators for the XXZ spin chain
• Energy transport in Heisenberg chains beyond the Luttinger liquid paradigm
• Typicality approach to the optical conductivity in thermal and many-body localized phases
• Energy transport between two integrable spin chains
• General Features of the Relaxation Dynamics of Interacting Quantum Systems
• Spin and energy currents in integrable and nonintegrable spin-1/2 chains: A typicality approach to real-time autocorrelations
• Universality classes of spin transport in one-dimensional isotropic magnets: the onset of logarithmic anomalies
• Extending the range of real time density matrix renormalization group simulations
• Real-time broadening of non-equilibrium density profiles and the role of the specific initial-state realization
• Transport properties of the one-dimensional Hubbard model at finite temperature
• Combining Dynamical Quantum Typicality and Numerical Linked Cluster Expansions
• Domain-wall melting as a probe of many-body localization
• Charges and currents in quantum spin chains: late-time dynamics and spontaneous currents
• Quasi-local conserved charges and spin transport in spin-$1$ integrable chains
• Random State Technology
• Spin and thermal conductivity of quantum spin ladders
• Low-Temperature Transport in Out-of-Equilibrium XXZ Chains
• Expansion potentials for exact far-from-equilibrium spreading of particles and energy
• Heat conductivity of the Heisenberg spin-1/2 ladder: From weak to strong breaking of integrability
• Lower bounds on high-temperature diffusion constants from quadratically extensive almost conserved operators
• Minimally entangled typical thermal states versus matrix product purifications for the simulation of equilibrium states and time evolution
• A class of states supporting diffusive spin dynamics in the isotropic Heisenberg model
• Proposal for measuring the finite-temperature Drude weight of integrable systems
• Matrix product purifications for canonical ensembles and quantum number distributions
• Finite-temperature charge transport in the one-dimensional Hubbard model
• Hubbard-to-Heisenberg crossover (and efficient computation) of Drude weights at low temperatures
• Real-Time Dynamics of Typical and Untypical States in Non-Integrable Systems
• Thermal conductivity of the one-dimensional Fermi-Hubbard model
• One-dimensional quantum systems at finite temperatures can be simulated efficiently on classical computers
• Low temperature dynamics of nonlinear Luttinger liquids
• Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet
• Absence of high-temperature ballistic transport in the spin-$1/2$ $XXX$ chain within the grand-canonical ensemble
• NMR relaxation in the spin-1 Heisenberg chain
• Quantum quenches, linear response and superfluidity out of equilibrium
• Spin transport through a spin-1/2 XXZ chain contacted to fermionic leads
• Energy dynamics in the Heisenberg-Kitaev chain
• Phase-induced transport in atomic gases: from superfluid to Mott insulator
• Popcorn Drude weights from quantum symmetry
• Spin rectification in thermally driven XXZ spin chain via the spin-Seebeck effect
• Finite-size anomalies of the Drude weight: role of symmetries and ensembles
• Extracting Nonlinear Dynamical Response Functions from Time Evolution
• Minimally entangled typical thermal states algorithm with Trotter gates
• Thermal Drude weight in an integrable chiral clock model
• Digital Quantum Simulation of Spin Transport
• Drude weight in hard core Boson systems: possibility of a finite temperature ideal conductor
• Energy transport in Z3 chiral clock model
• Quantum typicality approach to energy flow between two spin-chain domains at different temperatures